Pilot design for improved channel and interference estimation

ABSTRACT

Techniques for transmitting pilot and for processing received pilot to obtain channel and interference estimates are described. A terminal may generate pilot symbols for a first cluster in a time frequency block based on a first sequence and may generate pilot symbols for a second cluster in the time frequency block based on a second sequence. The first and second sequences may include common elements arranged in different orders and may be considered as different versions of a single sequence. The terminal may transmit the pilot symbols in their respective clusters. A base station may obtain received pilot symbols from multiple clusters in the time frequency block. The base station may form each of multiple basis vectors with multiple versions of the sequence assigned to the terminal and may process the received pilot symbols with the multiple basis vectors to obtain a channel estimate for the terminal.

The present application for patent is a Continuation of U.S. patentapplication Ser. No. 13/402,537 entitled “PILOT DESIGN FOR IMPROVEDCHANNEL AND INTERFERENCE ESTIMATION” filed Feb. 22, 2012, U.S. Pat. No.8,432,985, (Qualcomm Docket No. 061058D1) which claims priority to U.S.patent application Ser. No. 11/691,243 entitled “PILOT DESIGN FORIMPROVED CHANNEL AND INTERFERENCE ESTIMATION” filed Mar. 26, 2007, U.S.Pat. No. 8,130,867, (Qualcomm Docket No. 061058) which claims priorityto U.S. Provisional Application Ser. No. 60/883,756, entitled “PILOTDESIGN FOR IMPROVED SIMPLIFIED CHANNEL AND INTERFERENCE ESTIMATION WITHDEDICATED PILOT TONES FOR OFDMA” filed Jan. 5, 2007, (Qualcomm DocketNo. 061058P1) assigned to the assignee hereof and incorporated herein byreference.

BACKGROUND

I. Field

The present disclosure relates generally to communication, and morespecifically to a pilot design for a wireless communication system.

II. Background

A wireless multiple-access communication system can support multipleusers by sharing the available radio resources. Examples of suchmultiple-access systems include Code Division Multiple Access (CDMA)systems, Time Division Multiple Access (TDMA) systems, FrequencyDivision Multiple Access (FDMA) systems, Orthogonal FDMA (OFDMA)systems, and Single-Carrier FDMA (SC-FDMA) systems.

A wireless multiple-access system may support multiple-inputmultiple-output (MIMO) transmission on the forward and/or reverse link.On the reverse link (or uplink), one or more terminals may sendtransmissions from multiple (N_(T)) transmit antennas at the terminal(s)to multiple (N_(R)) receive antennas at a base station. A MIMO channelformed by the N_(T) transmit antennas and the N_(R) receive antennas maybe decomposed into N_(C) spatial channels, where N_(C)≦min {N_(T),N_(R)}. Improved performance (e.g., higher throughput and/or greaterreliability) may be achieved by exploiting the spatial channels formedby the multiple transmit and receive antennas.

For MIMO transmission on the reverse link, the wireless channel betweeneach terminal and the base station is normally estimated and used torecover the data transmission sent by the terminal via the wirelesschannel. Channel estimation is typically performed by sending pilot fromeach terminal and measuring the pilot at the base station. The pilot ismade up of symbols that are known a priori by both the terminal and thebase station. The base station can thus estimate the channel responsefor each terminal based on the pilot symbols received from that terminaland the known pilot symbols. Since pilot transmission representsoverhead, it is desirable to minimize pilot transmission to the extentpossible. However, the pilot transmission should be such that the basestation can obtain a good channel estimate for each terminal.

There is therefore a need in the art for techniques to send pilot suchthat a good channel estimate may be derived.

SUMMARY

Techniques for transmitting pilot and for processing received pilot toobtain channel and interference estimates are described herein. Atransmitter (e.g., a terminal) may generate pilot symbols for a firstcluster in a time frequency block (or tile) based on a first sequenceand may generate pilot symbols for a second cluster in the timefrequency block based on a second sequence. The transmitter may furthergenerate pilot symbols for a third cluster in the time frequency blockbased on the first sequence or a third sequence and may generate pilotsymbols for a fourth cluster in the time frequency block based on thesecond sequence or a fourth sequence. Each cluster may cover a group ofpilot symbols, typically adjacent to one another, in the time frequencyblock. The first, second, third and fourth sequences may include commonelements arranged in different orders and may be considered as differentversions of a single sequence. For example, the elements in the secondsequence may be in a reverse order (or flipped) with respect to theelements in the first sequence. The transmitter may transmit the pilotsymbols in their respective clusters in the time frequency block.

Multiple transmitters may share the time frequency block and may beassigned different sequences that are orthogonal to one another for eachcluster in the time frequency block. Each transmitter may generate pilotsymbols for each cluster based on the sequence assigned to thattransmitter for that cluster.

A receiver (e.g., a base station) may obtain received pilot symbols frommultiple clusters in the time frequency block. The receiver may formmultiple basis vectors for a transmitter, with each basis vector beingformed with multiple versions of a sequence assigned to thattransmitter. A basis vector is a vector of elements used for processingreceived symbols. The multiple versions of the sequence may correspondto different orderings of the elements in the sequence and may beconsidered as different sequences. The receiver may form the multiplebasis vectors further based on a particular channel model, e.g., achannel model with linearly varying time component and linearly varyingfrequency component. The receiver may process the received pilot symbolswith the multiple basis vectors to obtain a channel estimate for thetransmitter. The receiver may repeat the same processing (e.g., thegeneration of the basis vectors and the processing of the received pilotsymbols with the basis vectors) for each transmitter sharing the timefrequency block. The receiver may also obtain a noise and interferenceestimate based on the received pilot symbols and at least one basisvector not used for channel estimation.

Various aspects and features of the disclosure are described in furtherdetail below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of two terminals and a base station.

FIG. 2 shows a tile structure.

FIGS. 3A through 3D show designs of four pilot patterns.

FIG. 4 illustrates different combining options for four pilot clusters.

FIGS. 5A through 5D show use of multiple versions of a scramblingsequence to obtain symmetric pilot symbols for the four pilot patternsshown in FIGS. 3A through 3D.

FIG. 6 shows a process performed by a transmitter to transmit pilot.

FIG. 7 shows an apparatus for transmitting pilot.

FIG. 8 shows a process performed by a receiver to process receivedpilot.

FIG. 9 shows an apparatus for processing received pilot.

DETAILED DESCRIPTION

The techniques described herein may be used for various communicationsystems that support MIMO transmission and utilize a form of frequencydivision multiplexing (FDM). For example, the techniques may be used forsystems that utilize orthogonal FDM (OFDM), single-carrier FDM (SC-FDM),etc. OFDM and SC-FDM partition the system bandwidth into multiple (K)orthogonal subcarriers, which are also referred to as tones, bins, etc.Each subcarrier may be modulated with data. In general, modulationsymbols are sent in the frequency domain with OFDM and in the timedomain with SC-FDM. The techniques may also be used for transmissions onthe reverse link (or uplink) as well as the forward link (or downlink).For clarity, the techniques are described below for transmissions on thereverse link.

FIG. 1 shows a block diagram of a design of two terminals 110 x and 110y and a base station 150 in a wireless communication system. A terminalmay also be referred to as a user equipment (UE), a mobile station, anaccess terminal, a subscriber unit, a station, etc. A terminal may be acellular phone, a personal digital assistant (PDA), a wirelesscommunication device, a handheld device, a wireless modem, a laptopcomputer, a cordless phone, etc. A base station may also be referred toas a Node B, an evolved Node B (eNode B), an access point, etc. In FIG.1, terminal 110 x is equipped with a single antenna, terminal 110 y isequipped with multiple antennas, and base station 150 is equipped withmultiple antennas. Each antenna may be a physical antenna or an antennaarray. For simplicity, FIG. 1 shows only processing units for datatransmission on the reverse link and signaling transmission on theforward link.

At each terminal 110, a transmit (TX) data and pilot processor 120 mayreceive traffic data from a data source 112, process (e.g., format,encode, interleave, and symbol map) the traffic data, and generate datasymbols. Processor 120 may also generate and multiplex pilot symbolswith the data symbols. As used herein, a data symbol is a symbol fordata, a pilot symbol is a symbol for pilot, and a symbol is typically acomplex value. The data symbols and pilot symbols may be modulationsymbols from a modulation scheme such as PSK or QAM. Pilot is data thatis known a priori by both the terminals and the base station.

At terminal 110 y, a TX MIMO processor 122 y may perform transmitterspatial processing on the data and pilot symbols based on direct MIMOmapping, precoding, beamforming, etc. A data symbol may be sent from oneantenna for direct MIMO mapping or from multiple antennas for precodingand beamforming. Processor 122 y may provide N_(Y) streams of outputsymbols to N_(Y) modulators (MOD) 130 a through 130 ny. At terminal 110x, processor 120 x may provide a single output symbol stream to amodulator 130 x. Each modulator 130 may perform modulation (e.g., forOFDM, SC-FDM, etc.) on the output symbols to obtain output chips. Eachmodulator 130 may further process (e.g., convert to analog, filter,amplify, and upconvert) its output chips to generate a reverse linksignal. At terminal 110 x, a single reverse link signal from modulator130 x may be transmitted from antenna 132 x. At terminal 110 y, N_(Y)reverse link signals from modulators 130 a through 130 ny may betransmitted via N_(Y) antennas 132 a through 132 ny, respectively.

At base station 150, N_(R) antennas 152 a through 152 nr may receive thereverse link signals from terminals 110 x and 110 y and possibly otherterminals. Each antenna 152 may provide a received signal to arespective demodulator (DEMOD) 154. Each demodulator 154 may process(e.g., filter, amplify, downconvert, and digitize) its received signalto obtain samples and may further perform demodulation (e.g., for OFDM,SC-FDM, etc.) on the samples to obtain received symbols. Eachdemodulator 154 may provide received data symbols to a receive (RX)spatial processor 160 and may provide received pilot symbols to achannel processor 162. Channel processor 162 may estimate the responseof the wireless channel from each terminal 110 to base station 150 aswell as noise and interference based on the received pilot symbols. RXspatial processor 160 may perform MIMO detection on the received datasymbols with channel estimates and noise and interference estimates fromchannel processor 162 to obtain data symbol estimates. An RX dataprocessor 170 may process (e.g., deinterleave and decode) the datasymbol estimates and provide decoded data to a data sink 172.

Base station 150 may send traffic data and signaling (e.g., assignmentsof time frequency resources) to the terminals. The signaling may beprocessed by a TX signaling processor 174 and further processed bymodulators 154 a through 154 nr to generate N_(R) forward link signals,which may be transmitted via N_(R) antennas 152 a through 152 nr. Ateach terminal 110, the forward link signals from base station 150 may bereceived by one or more antennas 132, processed by one or moredemodulators 130, and further processed by an RX signaling processor 134to recover the signaling sent by base station 150.

Controllers/processors 140 x, 140 y, and 180 may control the operationof various processing units at terminals 110 x and 110 y and basestation 150, respectively. Memories 142 x, 142 y, and 182 may store dataand program codes for terminals 110 x and 110 y and base station 150,respectively. A scheduler 184 may schedule terminals for transmission onthe forward and/or reverse link.

FIG. 2 shows a tile structure 200 that may be used for the forwardand/or reverse link. The time frequency resources available for a givenlink may be partitioned into tiles, which may also be referred to astime frequency blocks, resource blocks, hop regions, etc. Each tile maycover multiple (F) subcarriers in multiple (T) symbol periods, where Fand T may each be any integer value. The F subcarriers in a given tilemay be consecutive subcarriers or may be distributed across the K totalsubcarriers. Each tile includes F·T resource units, where a resourceunit is one subcarrier in one symbol period. F·T modulation symbols maybe sent in the F·T resource units in each tile. Each tile may beassigned to one or more terminals for data transmission.

FIG. 2 also shows a frequency hopping scheme that may be used for theforward and/or reverse link. Frequency hopping may provide frequencydiversity against deleterious path effects and randomization ofinterference. With frequency hopping, a terminal may be assigned tilesin different parts of the system bandwidth in different hop periods. Ahop period is the time duration of one tile and spans T symbol periods.

Data and pilot may be sent in various manners in a tile. In one design,data and pilot symbols are sent in different resource units. The pilotsymbols may also be sent based on a pilot pattern that indicatesspecific resource units to use for the pilot symbols. In general, apilot pattern may include any number of pilot symbols, and the pilotsymbols may be located anywhere within a tile. The number of pilotsymbols may be selected based on a tradeoff between pilot overhead andchannel estimation performance. The spacing of the pilot symbols acrossfrequency may be selected based on expected delay spread of the wirelesschannel. Smaller frequency separation between pilot symbols may be usedto handle larger delay spread. The spacing of the pilot symbols acrosstime may be selected based on expected Doppler spread of the wirelesschannel. Smaller time separation between pilot symbols may be used tohandle larger Doppler spread.

The pilot symbols may also be placed to support spatial multiplexingtechniques such as MIMO and/or Spatial Division Multiple Access (SDMA).With spatial multiplexing, multiple data streams may be transmittedsimultaneously via multiple spatial channels or layers formed bymultiple transmit antennas and multiple receive antennas. To supportspatial multiplexing, the pilot symbols may be arranged in clusterswithin a tile. The number of pilot symbols (M) in each cluster may beequal to or larger than the spatial rank to be supported. Spatial rankrefers to the number of spatial channels, and hence the number of datastreams that may be transmitted in parallel. The pilot symbols in eachcluster may occupy a contiguous region in time and frequency such that,for each terminal, the variations of the wireless channel across thepilot symbols in one cluster are as small as possible.

FIG. 3A shows a design of a pilot pattern 310 for a 16×8 tile thatcovers F=16 subcarriers in T=8 symbol periods. In this design, the tileincludes 12 pilot symbols that are arranged in four clusters located atfour corners of the tile. The four clusters may be given indices of 1,2, 3 and 4, as shown in FIG. 3A. Each cluster includes M=3 pilot symbolssent on one subcarrier in three consecutive symbol periods. The threepilot symbols in each cluster may be used for channel estimation for upto three spatial channels.

FIG. 3B shows a design of a pilot pattern 320 for a 16×8 tile. In thisdesign, the tile includes 12 pilot symbols that are arranged in fourclusters located at four corners of the tile. Each cluster includes M=3pilot symbols sent on three consecutive subcarriers in one symbolperiod. The three pilot symbols in each cluster may be used for channelestimation for up to three spatial channels.

FIG. 3C shows a design of a pilot pattern 330 for a 16×8 tile. In thisdesign, the tile includes 16 pilot symbols that are arranged in fourclusters located at four corners of the tile. Each cluster includes M=4pilot symbols sent on two consecutive subcarriers in two consecutivesymbol periods. The four pilot symbols in each cluster may be used forchannel estimation for up to four spatial channels.

FIG. 3D shows a design of a pilot pattern 340 for a 16×8 tile. In thisdesign, the tile includes 24 pilot symbols that are arranged in eightclusters located in four rows of the tile. Each cluster includes M=3pilot symbols sent on one subcarrier in three consecutive symbolperiods. The three pilot symbols in each cluster may be used for channelestimation for up to three spatial channels.

FIGS. 3A to 3D show four example pilot patterns. Various other pilotpatterns may also be defined. In general, a pilot pattern may includeany number of clusters, and each cluster may include any number of pilotsymbols. Furthermore, the clusters and pilot symbols may be arranged inany manner in a tile. For clarity, much of the description below assumesthe use of pilot pattern 310 in FIG. 3A.

In general, one or more terminals may share a given tile. If the tilehas clusters of M pilot symbols, then up to M data streams may betransmitted on up to M spatial channels or layers. A terminal with asingle antenna (e.g., terminal 110 x in FIG. 1) may transmit a singledata stream on a single spatial channel. A terminal with multipleantennas (e.g., terminal 110 y in FIG. 1) may transmit multiple datastreams on multiple spatial channels.

For clarity, much of the following description assumes that Q terminalsshare a given tile, where 1≦Q≦M, and that each terminal transmits onedata stream on one spatial channel. The processing for this tile isdescribed below.

The base station may obtain F·T received symbols from the tile for the Qterminals. The received symbols may be expressed as:

$\begin{matrix}{{\underset{\_}{y} = {{\sum\limits_{q = 1}^{Q}{\Delta_{q}{{\underset{\_}{h}}_{q} \circ {\underset{\_}{z}}_{q}}}} + {\underset{\_}{n}}_{0}}},} & {{Eq}\mspace{14mu} (1)}\end{matrix}$

-   where z_(q) is an F·T×1 vector of modulation symbols transmitted by    terminal q on the F·T resource units in the tile,    -   h_(q) is an F·T×1 vector of complex channel gains for the F·T        resource units in the tile for terminal q,    -   Δ_(q) ² is a scalar for a power offset for terminal q,    -   y is an F·T×1 vector of received symbols for the F·T resource        units in the tile,    -   n₀ is an F·T×1 vector of noise and interference for the tile,        and    -   “^(o)” denotes an element-by-element multiply.

In equation (1), the first F elements of each vector correspond to the Fsubcarriers in the first symbol period of the tile, the next F elementscorrespond to the F subcarriers in the second symbol period, and so on,and the last F elements correspond to the F subcarriers in the lastsymbol period. h_(q) contains the frequency-domain complex channel gainsfor terminal q, which may be assumed to be complex Gaussian randomvariable with zero mean and a known covariance matrix. The channel gainsmay be assumed to be independent among the Q terminals. For simplicity,the noise and interference n₀ may be assumed to be additive whiteGaussian noise (AWGN) with a zero mean vector and a covariance matrix ofσ²I, where σ² is the variance of the noise and interference and I is theidentity matrix.

The base station may estimate the channel gains for each terminal aswell as the noise and interference based on the received pilot symbols.The base station may perform channel estimation based on an assumptionthat the statistical properties of the wireless channel for eachterminal are known and that the channel gains across the tile for eachterminal are correlated.

A covariance matrix for each terminal q, where q ε{1, . . . , Q}, may beapproximated as follows:

$\begin{matrix}{{{E\begin{Bmatrix}{\underset{\_}{h}}_{q} & {\underset{\_}{h}}_{q}^{H}\end{Bmatrix}} \approx {\sum\limits_{i = 1}^{3}{\lambda_{i,q}{\underset{\_}{u}}_{i}{\underset{\_}{u}}_{i}^{H}}}},} & {{Eq}\mspace{14mu} (2)}\end{matrix}$

where u_(i) is the i-th approximate eigenvector for the channel forterminal q,

λ_(i,q) is the i-th eigenvalue for the channel for terminal q,

E{ } denotes an expectation operation, and

“^(H)” denotes a Hermitian or complex transpose.

Equation (2) is based on an observation that, for cases of practicalinterest, the covariance matrix of a terminal has at most threesignificant eigenvalues and may be approximated with three eigenvectorsu₁, u₂ and u₃. These three approximate eigenvectors have dimension ofF·T×1 and may be used instead of the actual eigenvectors for channelestimation for terminal q across the tile. Furthermore, for the cases ofpractical interest, the first eigenvalue λ_(1,q) is typically at leastone order of magnitude larger than the other two eigenvalues λ_(2,q) andλ_(3,q).

The three approximate eigenvectors may be expressed as:

$\begin{matrix}{{{{\underset{\_}{u}}_{1} = {{\underset{\_}{u}}_{T,0} \otimes {\underset{\_}{u}}_{F,0}}},{{\underset{\_}{u}}_{2} = {{\underset{\_}{u}}_{T,0} \otimes {\underset{\_}{u}}_{F,1}}},{{\underset{\_}{u}}_{3} = {{\underset{\_}{u}}_{T,1} \otimes {\underset{\_}{u}}_{F,0}}},{where}}{{\underset{\_}{u}}_{F,0} = {\frac{1}{\sqrt{F}}\left\lbrack {1,\ldots \mspace{14mu},1} \right\rbrack}^{T}}\mspace{20mu} {{F \times 1\mspace{14mu} {vector}},{{\underset{\_}{u}}_{F,1} = {\sqrt{\frac{3}{F \cdot \left( {F^{2} - 1} \right)}}\left\lbrack {{- \left( {F - 1} \right)}\text{:}2\text{:}\left( {F - 1} \right)} \right\rbrack}^{T}}}\mspace{20mu} {{F \times 1\mspace{14mu} {vector}},{{\underset{\_}{u}}_{T,0} = {\frac{1}{\sqrt{T}}\left\lbrack {1,\ldots \mspace{14mu},1} \right\rbrack}^{T}}}{{T \times 1\mspace{14mu} {vector}},{{\underset{\_}{u}}_{T,1} = {\sqrt{\frac{3}{T \cdot \left( {T^{2} - 1} \right)}}\left\lbrack {{- \left( {T - 1} \right)}\text{:}2\text{:}\left( {T - 1} \right)} \right\rbrack}^{T}}}{{T \times 1\mspace{14mu} {vector}},{and}}{{`` \otimes "}\mspace{14mu} {denotes}\mspace{14mu} a\mspace{14mu} {Kronecker}\mspace{14mu} {{product}.}}} & {{Eq}\mspace{14mu} (3)}\end{matrix}$

For an n×1 vector a_(n×1)=[a₁, a₂, . . . , a_(n)]^(T) and an m×1 vectorb_(m×1)=[b₁, b₂, . . . , b_(m)]^(T), where “^(T)” denotes a transpose,the Kronecker product c_(mn×1)=a_(n×1)

b_(m×1) may be given as:

$\begin{matrix}{{\underset{\_}{c}}_{{mn} \times 1} = \begin{bmatrix}{a_{1}{\underset{\_}{b}}_{m \times 1}} \\{a_{2}{\underset{\_}{b}}_{m \times 1}} \\\vdots \\{a_{n}{\underset{\_}{b}}_{m \times 1}}\end{bmatrix}} \\{= {\begin{bmatrix}{{a_{1}b_{1}},{a_{1}b_{2}},\ldots \mspace{14mu},{a_{1}b_{m}},{a_{2}b_{1}},{a_{2}b_{2}},\ldots \mspace{14mu},} \\{{a_{2}b_{m}},\ldots \mspace{14mu},{a_{n}b_{1}},{a_{n}b_{2}},\ldots \mspace{14mu},{a_{n}b_{m}}}\end{bmatrix}^{T}.}}\end{matrix}$

c_(mn×1) is an mn×1 vector containing the product of each element ofa_(n×1) with each element of b_(m×1).

In equation (3), u_(F,0) is a vector of all ones, scaled by a constantto achieve unit power for u_(F,0). u_(F,1) is a vector with values from−(F−1) to (F−1) in steps of 2, scaled by a constant to achieve unitpower for u_(F,1). u_(F,1) varies linearly across the F subcarriers ofthe tile. u_(T,0) is a vector of all ones, scaled by a constant toachieve unit power for u_(T,0). u_(T,1) is a vector with values from−(T−1) to (T−1) in steps of 2, scaled by a constant to achieve unitpower for u_(T,1). u_(T,1) varies linearly across the T symbol periodsof the tile.

u₁ is an F·T×1 vector of all ones, scaled by a constant to achieve unitpower for u₁. u₂ is an F·T×1 vector containing T sequences of the Felements in u_(F,1), scaled by a constant to achieve unit power for u₂.u₃ is an F·T×1 vector containing F repetitions of each of the T elementsin u_(T,1), scaled by a constant to achieve unit power for u₃. u₁ modelsDC or average component. u₂ models variation of the channel infrequency. u₃ models variation of the channel in time.

The channel response of each terminal q across the tile may be modeledas a random function of frequency and time, ξ_(q) (f,t). This functionmay be approximated by the first three terms of the Taylor seriesexpansion, as follows:

$\begin{matrix}{{\xi_{q}\left( {f,t} \right)} \approx {{\xi_{q}\left( {f_{0},t_{0}} \right)} + {{\left( {f - f_{0}} \right) \cdot \frac{\partial{\xi_{q}\left( {f,t} \right)}}{\partial f}}{{_{({f_{0},t_{0}})}{{+ \left( {t - t_{0}} \right)} \cdot \frac{\partial{\xi_{q}\left( {f,t} \right)}}{\partial t}}}_{({f_{0},t_{0}})}.}}}} & {{Eq}\mspace{14mu} (4)}\end{matrix}$

In equation (4), the 2-dimensional (2D) function ξ_(q)(f,t) isapproximated with (i) a first term for the value of ξ_(q)(f,t) at theorigin, or ξ_(q)(f₀, t₀), (ii) a second term for a linear functionacross frequency, or S_(F,q)·(f−f₀), and (iii) a third term for a linearfunction across time, or S_(T,q)·(t−t₀). The slopes S_(F,q) and S_(T,q)of the linear functions across frequency and time are determined by theslope of ξ_(q)(f,t) with respect to frequency and time, respectively, atthe origin.

Based on the channel model shown in equation (4), the channel responseof terminal q may be expressed as:

h _(q)(n _(f) ,n _(t))≈α_(q)+β_(F,q)·(n _(f) −n _(f0))+β_(T,q)·(n ₁ −n_(t0)),  Eq (5)

where α_(q) is an average channel gain, which corresponds to the termξ_(q)(f₀, t₀),

β_(F,q) is the slope of the linear function across frequency forterminal q,

β_(T,q) is the slope of the linear function across time for terminal q,and

h_(q)(n_(f),n_(t)) is a 2D function for the channel response of terminalq.

As shown in equation (5), the channel response of terminal q across thetile may be characterized by three complex parameters α_(q), β_(F,q) andβ_(T,q). The center of the tile may be given as (n_(f0),n_(t0)), wheren_(f0)=(F+1)/2 and n_(t0)=(T+1)/2. The channel response for a symbol atdiscrete coordinates (n_(f),n_(t)) may be obtained as shown in equation(5).

A pilot pattern may include P total pilot symbols that may be arrangedin four clusters, with each cluster including M pilot symbols, so thatP=4M. The pilot symbols may be placed at locations that are symmetricabout the center of the tile, e.g., as shown in FIGS. 3A through 3D. Ifeach terminal transmits one data stream on one spatial channel, then thenumber of terminals that can share the tile is limited to M, or Q≦M.

The Q terminals may share a cluster, and each of the Q terminals maysimultaneously transmit M pilot symbols in that cluster. Each terminalmay scramble or spread its M pilot symbols with a scrambling sequenceassigned to that terminal. The scrambling sequences for the Q terminalsmay be denoted as s_(q), for q=1, . . . , Q, and should be orthogonal toone another. The scrambling sequences may also be referred to asspreading sequences, orthogonal sequences, pilot sequences, sequences,etc. The scrambling sequences may have unit modulus elements and shouldbe of length of M. In one design, M scrambling sequences are definedbased on M columns of an M×M Fourier matrix, with each scramblingsequence containing M elements of one column of the Fourier matrix. Theelement in the n-th row and m-th column of the M×M Fourier matrix may begiven as e^(−2π·n·m/M), for n=0, . . . , M−1 and m=0, . . . , M−1. The Mscrambling sequences may also be defined in other manners. In any case,Q scrambling sequences may be selected from among the M availablescrambling sequences. In one design, each terminal is assigned onescrambling sequence and uses the same scrambling sequence for allclusters in the tile. In another design, each terminal may use differentscrambling sequences for different clusters in the tile.

The pilot symbols transmitted by terminal q in the tile may be expressedas:

$\begin{matrix}{{{\underset{\_}{r}}_{1,q} = {\frac{1}{\sqrt{P}} \cdot {{\underset{\_}{1}}_{4 \times 1} \otimes {\underset{\_}{s}}_{q}}}},} & {{Eq}\mspace{14mu} (6)}\end{matrix}$

where 1_(4×1) is a 4×1 vector of all ones, and

r_(1,q) is a P×1 vector of pilot symbols transmitted by terminal q inthe tile.

The first M elements of r_(1,q) are for pilot symbols sent in cluster 1in the upper-left corner of the tile, the next M elements are for pilotsymbols sent in cluster 2 in the upper-right corner, the next M elementsare for pilot symbols sent in cluster 3 in the lower-left corner, andthe last M elements are for pilot symbols sent in cluster 4 in thelower-right corner. The pilot vectors r_(1,q) for terminals 1 through Qare orthonormal.

FIG. 3A shows the transmitted pilot symbols for pilot pattern 310 withscrambling sequence s_(q)=[a b c]^(T), where a, b and c are threeelements of the scrambling sequence and may have any complex values. Thethree elements a, b and c in s_(q) are applied to three pilot symbolsfrom left to right in each cluster in the tile.

FIG. 3B shows the transmitted pilot symbols for pilot pattern 320 withscrambling sequence s_(q)=[a b c]^(T). The three elements a, b and c ins_(q) are applied to three pilot symbols from top to bottom in eachcluster in the tile.

FIG. 3C shows the transmitted pilot symbols for pilot pattern 330 withscrambling sequence s_(q)=[a b c d]^(T). The four elements a, b, c and din s_(q) are applied to four pilot symbols in a z-pattern in eachcluster in the tile.

FIG. 3D shows the transmitted pilot symbols for pilot pattern 340 withscrambling sequence s_(q)=[a b c]^(T). The three elements a, b and c ins_(q) are applied to three pilot symbols from left to right in eachcluster in the tile.

A set of basis vectors may be defined for each terminal q, as follows:

$\begin{matrix}{{{\underset{\_}{r}}_{i,q} = {\frac{1}{\sqrt{P}} \cdot {{\underset{\_}{v}}_{i} \otimes {\underset{\_}{s}}_{q}}}},{{{where}\mspace{14mu} {\underset{\_}{v}}_{1}} = \begin{bmatrix}1 \\1 \\1 \\1\end{bmatrix}},{{\underset{\_}{v}}_{2} = \begin{bmatrix}{- 1} \\{- 1} \\1 \\1\end{bmatrix}},{{\underset{\_}{v}}_{3} = \begin{bmatrix}{- 1} \\1 \\{- 1} \\1\end{bmatrix}},{{\underset{\_}{v}}_{4} = {\begin{bmatrix}1 \\{- 1} \\{- 1} \\1\end{bmatrix}.}}} & {{Eq}\mspace{14mu} (7)}\end{matrix}$

FIG. 4 illustrates vectors v₁ through v₄. The four vectors v₁ through v₄have different combinations of signs for the four clusters in the tileand represent different combining options for the pilot symbols receivedin the four clusters, as described below.

Each terminal q is associated with a set of four P×1 basis vectorsr_(1,q), r_(2,q), r_(3,q) and r_(4,q). r_(1,q) contains the transmittedpilot symbols. r_(2,q) is generated with v₂ and is used to detectchannel variation across frequency. r_(3,q) is generated with v₃ and isused to detect channel variation across time. r_(4,q) is generated withv₄ and may be used for noise and interference estimation.

If the number of degrees of freedom of the channels for the Q terminalssharing the tile is lower than the total number of pilot symbols in thetile, then pilot symbols not used to estimate parameters of the channelsmay be used to estimate noise and interference power in the tile. Theobservation space has P dimensions corresponding to the P total pilotsymbols in the tile. In the design described above, the channel of eachterminal may be characterized by three parameters, and 3Q dimensions maybe used to estimate the channel parameters for all Q terminals. Theremaining P−3Q dimensions of the observation space may be used toestimate noise and interference power.

The noise and interference may be estimated as the power of theprojection of a received signal onto dimensions not occupied by pilotsignals transmitted by the Q terminals. The received signal may beprojected onto the basis vectors for all M available scramblingsequences, as follows:

w _(i,q) =r _(i,q) ^(H) x, for i=1, . . . ,4 and q=1, . . . ,M ,  Eq (8)

where x is a P×1 vector with P received pilot symbols in the tile, and

w_(i,q) is the result of the projection of received vector x onto basisvector r_(i,q).

For each terminal q, equation (8) effectively despreads the M receivedpilot symbols in each cluster with the scrambling sequence s_(q) forthat terminal q. Equation (8) further accumulates the four despreadresults for the four clusters in different manners for different basisvectors. Referring to FIG. 4, for r_(1,q), the despread results for thefour clusters are summed to obtain w_(1,q), which is indicative of anaverage channel gain for terminal q. For r_(2,q), the despread resultsfor the two upper clusters are subtracted from the despread results forthe two lower clusters to obtain w_(2,q), which is indicative of channelvariation across frequency for terminal q. For r_(3,q), the despreadresults for the two left clusters are subtracted from the despreadresults for the two right clusters to obtain w_(3,q), which isindicative of channel variation across time for terminal q. For r_(3,q),the despread results for the upper-right and lower-left clusters aresubtracted from the despread results for upper-left and lower-rightclusters to obtain w_(4,q).

The noise and interference power may be estimated as follows:

$\begin{matrix}{{{\hat{\sigma}}^{2} = {\frac{1}{{4M} - {3Q}} \cdot \left( {{\sum\limits_{q = 1}^{Q}{w_{4,q}}^{2}} + {\sum\limits_{i = 1}^{4}{\sum\limits_{q = {Q + 1}}^{M}{w_{i,q}}^{2}}}} \right)}},} & {{Eq}\mspace{14mu} (9)}\end{matrix}$

where {circumflex over (σ)}² is the estimated noise and interferencepower.

In equation (9), the first summation captures the power of theprojection of x onto r_(4,q), which is not used for channel estimationfor any terminal. The first summation may be used as an estimate of thenoise and interference power but may include channel modeling error ifthe channel of each terminal does not vary linearly across the tile. Thedouble summation captures the power of the projection of x onto r_(i,q)generated with scrambling sequences not used by any of the Q terminals.The double summation is present if Q<M.

A channel estimate may be derived for each terminal q based on minimummean square error (MMSE) criterion, as follows:

ĥ _(q) =E{h _(q) x ^(H)}(E{xx ^(H)})⁻¹ x,  Eq (10)

where ĥ_(q) is an F·T×1 vector for the channel estimate for terminal q.ĥ_(q) is an estimate of h_(q) in equation (1).

Using the channel model shown in equation (2), the channel estimate foreach terminal q may be expressed as:

$\begin{matrix}{{{{\Delta_{q}{\hat{\underset{\_}{h}}}_{q}} = {\sum\limits_{i = 1}^{3}{{\frac{\Delta_{q}^{2} \cdot \lambda_{i,q} \cdot \rho_{i}}{{\Delta_{q}^{2} \cdot \lambda_{i,q} \cdot \rho_{i}^{2}} + {\hat{\sigma}}^{2}} \cdot w_{i,q}}{\underset{\_}{u}}_{i}}}},{{{where}\mspace{14mu} \rho_{1}} = \left( \sqrt{\frac{F \cdot T}{P}} \right)^{- 1}},{\rho_{2} = \left( {\sqrt{\frac{F \cdot T \cdot \left( {F^{2} - 1} \right)}{3P}} \cdot \frac{1}{F - \theta_{F}}} \right)^{- 1}},{and}}{\rho_{3} = {\left( {\sqrt{\frac{F \cdot T \cdot \left( {T^{2} - 1} \right)}{3P}} \cdot \frac{1}{T - \theta_{T}}} \right)^{- 1}.}}} & {{Eq}\mspace{14mu} (11)}\end{matrix}$

θ_(T) and θ_(F) identify the center of the pilot clusters in the tileand are thus dependent on the placement of the pilot symbols in thetile. The center of the upper-left cluster may be given by

$\left( {\frac{\theta_{T} + 1}{2},\frac{\theta_{F} + 1}{2}} \right).$

For example, θ_(F)=1 if the pilot symbols are placed in the topmost rowof the tile, θ_(F)=3 if the pilot symbols are placed in the secondtopmost row, etc.

In equation (11), the channel estimate ĥ_(q) for terminal q may beobtained based on a sum of three weighted vectors, where u₁, u₂ and u₃are defined in equation (3). The weight for u_(i) is determined byparameter ρ_(i), eigenvalue λ_(i,q), power offset Δ_(q) ², noise andinterference estimate {circumflex over (σ)}², and projection resultw_(i,q). The eigenvalues λ_(i,q) may be estimated in any manner known inthe art.

An assumption used in deriving the channel estimate is that the channelof each terminal is constant for the M pilot symbols in each cluster. Ifthe channel varies across the M pilot symbols in each cluster, then thedescrambling/despreading may have residual errors that may degrade thechannel estimate.

To see the effects of despreading errors, equation (8) may be expandedas follows:

$\begin{matrix}\begin{matrix}{w_{i,q} = {{\underset{\_}{r}}_{i,q}^{H}\underset{\_}{x}}} \\{= {{\underset{\_}{r}}_{i,q}^{H}\left\lbrack {{\sum\limits_{k = 1}^{Q}{\Delta_{k}{{\overset{\sim}{\underset{\_}{h}}}_{k} \circ {\underset{\_}{r}}_{1,k}}}} + {\overset{\sim}{n}}_{0}} \right\rbrack}} \\{{= {{\Delta_{q}{{\underset{\_}{r}}_{i,q}^{H}\left( {{\overset{\sim}{\underset{\_}{h}}}_{q} \circ {\underset{\_}{r}}_{1,q}} \right)}} + {{\underset{\_}{r}}_{i,q}^{H}{\sum\limits_{{k = 1},{k \neq q}}^{Q}{\Delta_{k}{{\overset{\sim}{\underset{\_}{h}}}_{k} \circ {\underset{\_}{r}}_{1,k}}}}} + {{\underset{\_}{r}}_{i,q}^{H}{\overset{\sim}{\underset{\_}{n}}}_{0}}}},}\end{matrix} & {{Eq}\mspace{14mu} (12)}\end{matrix}$

where {tilde over (h)}_(k) is a P×1 vector of complex channel gains forterminal k for the P pilot symbols, and ñ₀ is a P×1 vector of noise andinterference for the P pilot symbols. {tilde over (h)}_(k) contains Pelements in h_(k) for the P pilot symbols, and ñ₀ contains P elements inn₀ for the P pilot symbols.

As shown in equation (12), projection result w_(i,q) for terminal qincludes a component from terminal q as well as contributions from otherterminals and noise. The contribution n_(i,q,k) from another terminal kin the projection result w_(i,q) for terminal q may be expressed as:

n _(i,q,k) =r _(i,q) ^(H)({tilde over (h)} _(k) ∘r _(1,k)), wherek≠q.  Eq (13)

If the despreading is perfect, then n_(i,q,k)=0 for all other terminals,and no contributions from other terminals appear in the projectionresult w_(i,q) for terminal q. However, the contributions from otherterminals are non-zero when their channels vary across the M pilotsymbols in a cluster.

Based on the channel model in equation (5), the channel response of eachterminal k may be expressed as:

{tilde over (h)} _(k)≈α_(k)·(v ₁

1_(M×1))+2β_(F,k)·(n _(f) −n _(f0))·(v ₂

1_(M×1))+2β_(T,k) ·v _(T).  Eq (14)

For the pilot pattern shown in FIG. 3A, v_(T) may be given as:

$\begin{matrix}{{\underset{\_}{v}}_{T} = {{\begin{bmatrix}1 \\1\end{bmatrix} \otimes \begin{bmatrix}{- 7} \\{- 5} \\{- 3} \\3 \\5 \\7\end{bmatrix}} = {{5\; {{\underset{\_}{v}}_{3} \otimes {\underset{\_}{1}}_{M \times 1}}} + {{\underset{\_}{v}}_{1} \otimes {\begin{bmatrix}{- 2} \\0 \\2\end{bmatrix}.}}}}} & {{Eq}\mspace{14mu} (15)}\end{matrix}$

Combining equations (6) and (14), term √{square root over (P)}·{tildeover (h)}_(k)∘r_(1,q) may be expressed as:

$\begin{matrix}{{{\sqrt{P} \cdot {{\overset{\sim}{\underset{\_}{h}}}_{k} \circ {\underset{\_}{r}}_{1,q}}} \approx {{\alpha_{k} \cdot \left( {{\underset{\_}{v}}_{1} \otimes {\underset{\_}{s}}_{k}} \right)} + {2{\beta_{F,k} \cdot \left( {n_{f} - n_{f\; 0}} \right) \cdot \left( {{\underset{\_}{v}}_{2} \otimes {\underset{\_}{s}}_{k}} \right)}} + {2{\beta_{T,k} \cdot {\underset{\_}{p}}_{k}}}}},\mspace{79mu} {{{where}\mspace{14mu} {\underset{\_}{p}}_{k}} = {{5\; {{\underset{\_}{v}}_{3} \otimes {\underset{\_}{s}}_{k}}} + {\underset{\_}{\theta}}_{k}}},{{\underset{\_}{\theta}}_{k} = {{\underset{\_}{v}}_{1} \otimes {\underset{\_}{e}}_{k}}},{{\underset{\_}{e}}_{k} = {\left( {\begin{bmatrix}{- 2} \\0 \\2\end{bmatrix} \circ {\underset{\_}{s}}_{k}} \right).}}} & {{Eq}\mspace{14mu} (16)}\end{matrix}$

The contribution from terminal k may then be expressed as:

$\begin{matrix}\begin{matrix}{{P \cdot n_{i,q,k}} = {P \cdot {{\underset{\_}{r}}_{i,q}^{H}\left( {{\overset{\sim}{\underset{\_}{h}}}_{k} \circ {\underset{\_}{r}}_{1,k}} \right)}}} \\{= {{{\alpha_{k} \cdot \begin{pmatrix}{\underset{\_}{v}}_{i}^{H} & {\underset{\_}{v}}_{1}\end{pmatrix}}\begin{pmatrix}{\underset{\_}{s}}_{q}^{H} & {\underset{\_}{s}}_{k}\end{pmatrix}} + {2{\beta_{F,k} \cdot}}}} \\{{{{\left( {n_{f} - n_{f\; 0}} \right) \cdot \begin{pmatrix}{\underset{\_}{v}}_{i}^{H} & {\underset{\_}{v}}_{2}\end{pmatrix}}\begin{pmatrix}{\underset{\_}{s}}_{q}^{H} & {\underset{\_}{s}}_{k}\end{pmatrix}} +}} \\{{{2{\beta_{T,k} \cdot \left( {n_{t} - n_{t\; 0}} \right) \cdot \begin{pmatrix}{\underset{\_}{v}}_{i}^{H} & {\underset{\_}{v}}_{3}\end{pmatrix}}\begin{pmatrix}{\underset{\_}{s}}_{q}^{H} & {\underset{\_}{s}}_{k}\end{pmatrix}} +}} \\{{2{\beta_{T,k} \cdot \left( {{\underset{\_}{v}}_{i}^{H} \otimes {\underset{\_}{s}}_{q}^{H}} \right)}{{\underset{\_}{\theta}}_{k}.}}}\end{matrix} & {{Eq}\mspace{14mu} (17)}\end{matrix}$

The scrambling sequences for the Q terminals are orthogonal, so that:

s _(q) ^(H) s _(k)=δ_(q,k).  Eq (18)

Equation (18) indicates that the dot product of s_(q) with s_(k) isequal to 1.0 when q=k and is equal to 0.0 otherwise.

Vectors v₁ through v₄ are also orthogonal, so that:

v _(i) ^(H) v _(k)=4δ_(i,k).  Eq (19)

Equation (17) may then be simplified as follows:

P·n _(i,q,k)=2β_(T,k)·(v _(i) ^(H)

s_(q) ^(H))θ_(k)=2β_(T,k)·(v _(i) ^(H) v ₁)(s _(q) ^(H) e _(k))  Eq (20)

Equation (20) indicates that for terminal q, time variation in thechannel of another terminal k introduces an error or bias n_(i,q,k) inthe projection result w_(i,q,k) for terminal q. This error is due to thefact that s_(q) ^(H)e_(k)≠0 if k≠q.

To mitigate the error contributions from other terminals, the scramblingsequence for terminal q may be applied in a symmetric manner about thecenter of the tile. For the pilot pattern shown in FIG. 3A, a flippedscrambling sequence

of length 3 may be defined for terminal q, as follows:

$\begin{matrix}{{\underset{\_}{s}}_{q}^{\updownarrow} = {\begin{bmatrix}0 & 0 & 1 \\0 & 1 & 0 \\1 & 0 & 0\end{bmatrix}{{\underset{\_}{s}}_{q}.}}} & {{Eq}\mspace{14mu} (21)}\end{matrix}$

If each cluster includes M=3 pilot symbols, then the original andflipped scrambling sequences for terminal q may be given as:

s _(q) =[abc] ^(T), original scrambling sequence, and  Eq (22)

=cba]^(T), flipped scrambling sequence.

The original scrambling sequence may be used for the two clusters to theleft of the tile center, and the flipped scrambling sequence may be usedfor the two clusters to the right of the tile center. The original andflipped scrambling sequences may also be considered as two versions ofthe same scrambling sequence.

FIG. 5A shows use of the original and flipped scrambling sequences forthe pilot pattern shown in FIG. 3A. In this example, elements a, b and cin the original scrambling sequence s_(q) are applied to three pilotsymbols from left to right in each cluster to the left of the tilecenter. Elements c, b and a in the flipped scrambling sequence

are applied to three pilot symbols from left to right in each cluster tothe right of the tile center. The pilot symbols are symmetric about thecenter of the tile. This pilot symmetry reduces error in the channelestimate for terminal q.

FIG. 5B shows use of the original and flipped scrambling sequences forthe pilot pattern shown in FIG. 3B. In this example, elements a, b and cin the original scrambling sequence s_(q) are applied to three pilotsymbols from top to bottom in each cluster above the tile center.Elements c, b and a in the flipped scrambling sequence

are applied to three pilot symbols from top to bottom in each clusterbelow the tile center. The pilot symbols are symmetric about the centerof the tile.

FIG. 5C shows use of four versions of the scrambling sequence for thepilot pattern shown in FIG. 3C. In this example, each cluster includesM=4 pilot symbols, and four versions of the scrambling sequence may begiven as:

s _(q) =[abcd] ^(T), first version of the scrambling sequence,  Eq (23)

s _(q2) =[badc] ^(T), second version of the scrambling sequence,

s _(q3) =[cdab] ^(T), third version of the scrambling sequence, and

s_(q4) =[dcba] ^(T), fourth version of the scrambling sequence.

Elements a, b, c and d in the first version s_(q) are applied to fourpilot symbols in a z-pattern in the upper-left cluster. Elements b, a, dand c in the second version s_(q2) are applied to four pilot symbols ina z-pattern in the upper-right cluster. Elements c, d, a and b in thethird version s_(q3) are applied to four pilot symbols in a z-pattern inthe lower-left cluster. Elements d, c, b and a in the fourth versions_(q4) are applied to four pilot symbols in a z-pattern in thelower-right cluster. The pilot symbols are symmetric about the center ofthe tile.

FIG. 5D shows use of the original and flipped scrambling sequences forthe pilot pattern shown in FIG. 3D. In this example, elements a, b and cin the original scrambling sequence s_(q) are applied to three pilotsymbols from left to right in each cluster to the left of the tilecenter. Elements c, b and a in the flipped scrambling sequence

are applied to three pilot symbols from left to right in each cluster tothe right of the tile center. The pilot symbols are symmetric about thecenter of the tile.

FIGS. 5A through 5D show four examples in which multiple versions of thescrambling sequence are used to obtain pilot symbols that are symmetricwith respect to the center of the tile. In general, any number ofversions of the scrambling sequence may be used to achieve symmetricpilot symbols, depending on how the clusters are defined. All versionsof the scrambling sequence may have the same elements, but theseelements may be arranged in different orders in different versions.

For the pilot pattern shown in FIG. 5A, using the original and flippedscrambling sequences shown in equation (24), basis vectors r_(i,q) fori=1, . . . , 4 may be expressed as:

$\begin{matrix}{{{\underset{\_}{r}}_{1,q} = {\frac{1}{\sqrt{P}}\begin{bmatrix}{\underset{\_}{s}}_{q} \\{\underset{\_}{s}}_{q}^{\updownarrow} \\{\underset{\_}{s}}_{q} \\{\underset{\_}{s}}_{q}^{\updownarrow}\end{bmatrix}}},{{\underset{\_}{r}}_{2,q} = {\frac{1}{\sqrt{P}}\begin{bmatrix}{- {\underset{\_}{s}}_{q}} \\{- {\underset{\_}{s}}_{q}^{\updownarrow}} \\{\underset{\_}{s}}_{q} \\{\underset{\_}{s}}_{q}^{\updownarrow}\end{bmatrix}}},{{\underset{\_}{r}}_{3,q} = {\frac{1}{\sqrt{P}}\begin{bmatrix}{- {\underset{\_}{s}}_{q}} \\{\underset{\_}{s}}_{q}^{\updownarrow} \\{- {\underset{\_}{s}}_{q}} \\{\underset{\_}{s}}_{q}^{\updownarrow}\end{bmatrix}}},{{\underset{\_}{r}}_{4,q} = {{\frac{1}{\sqrt{P}}\begin{bmatrix}{\underset{\_}{s}}_{q} \\{- {\underset{\_}{s}}_{q}^{\updownarrow}} \\{- {\underset{\_}{s}}_{q}} \\{\underset{\_}{s}}_{q}^{\updownarrow}\end{bmatrix}}.}}} & {{Eq}\mspace{14mu} (24)}\end{matrix}$

Channel estimation and noise and interference estimation for terminal qmay be performed in the manner described above, albeit with the basisvectors r_(i,q) being defined as shown in equation (24) instead ofequation (7). The contribution from another terminal k to the projectionresult w_(i,q,k) for terminal q may be expressed as:

$\begin{matrix}{n_{i,q,k} = {{{\underset{\_}{r}}_{i,q}^{H}\left( {{\overset{\sim}{\underset{\_}{h}}}_{k} \circ {\underset{\_}{r}}_{1,k}} \right)} = \begin{matrix}{\underset{\_}{r}}_{i,q}^{H} & {{\underset{\_}{\theta}}_{k},}\end{matrix}}} & {{Eq}\mspace{14mu} (25)} \\{{{where}\mspace{14mu} {\underset{\_}{\theta}}_{k}} = {{\begin{bmatrix}{\underset{\_}{e}}_{q} \\{- {\underset{\_}{e}}_{q}^{\updownarrow}} \\{\underset{\_}{e}}_{q} \\{- {\underset{\_}{e}}_{q}^{\updownarrow}}\end{bmatrix}\mspace{14mu} {and}\mspace{14mu} {\underset{\_}{e}}_{q}^{\updownarrow}} = {{\begin{bmatrix}{- 2} \\0 \\2\end{bmatrix} \circ {\underset{\_}{s}}_{q}^{\updownarrow}} = {- {{\underset{\_}{e}}_{q}^{\updownarrow}.}}}}} & \;\end{matrix}$

It can be shown that n_(i,q,k)=0 for i=1, 2, and 4 due to flipping ofthe scrambling sequence. n_(3,q,k) may not be equal to 0 even withflipping, which means that there may be an error affecting w_(3,q) forthe time-varying component of the channel. Nevertheless, the errorintroduced in the channel estimate is smaller with flipping because ofmultiplication by an MMSE ratio corresponding to the time-varyingcomponent.

For the pilot pattern shown in FIG. 5D, using four versions of thescrambling sequence shown in equation (23), basis vectors r_(i,q) fori=1, . . . , 4 may be expressed as:

$\begin{matrix}{{{\underset{\_}{r}}_{1,q} = {\frac{1}{\sqrt{P}}\begin{bmatrix}{\underset{\_}{s}}_{q} \\{\underset{\_}{s}}_{q\; 2} \\{\underset{\_}{s}}_{q\; 3} \\{\underset{\_}{s}}_{q\; 4}\end{bmatrix}}},{{\underset{\_}{r}}_{2,q} = {\frac{1}{\sqrt{P}}\begin{bmatrix}{- {\underset{\_}{s}}_{q}} \\{- {\underset{\_}{s}}_{q\; 2}} \\{\underset{\_}{s}}_{q\; 3} \\{\underset{\_}{s}}_{q\; 4}\end{bmatrix}}},{{\underset{\_}{r}}_{3,q} = {\frac{1}{\sqrt{P}}\begin{bmatrix}{- {\underset{\_}{s}}_{q}} \\{\underset{\_}{s}}_{q\; 2} \\{- {\underset{\_}{s}}_{q\; 3}} \\{\underset{\_}{s}}_{q\; 4}\end{bmatrix}}},{{\underset{\_}{r}}_{4,q} = {{\frac{1}{\sqrt{P}}\begin{bmatrix}{\underset{\_}{s}}_{q} \\{- {\underset{\_}{s}}_{q\; 2}} \\{- {\underset{\_}{s}}_{q\; 3}} \\{\underset{\_}{s}}_{q\; 4}\end{bmatrix}}.}}} & {{Eq}\mspace{14mu} (26)}\end{matrix}$

Computer simulations show that for high signal-to-noise-and-interferenceratio (SINR), the floor of the channel estimation error may decrease byapproximately 2 decibels (dB) for vehicular channels with the pilotpattern shown in FIG. 5A. This may improve packet error rate and dataperformance.

For clarity, the techniques have been described for pilot transmissionon the reverse link and for channel and interference estimation forterminals. The techniques may also be used for pilot transmission on theforward link and for channel estimation for a base station. On theforward link, different spatial channels or layers may be assigneddifferent scrambling sequences. The processing for the different layerson the forward link may be analogous to the processing for differentterminals on the reverse link.

FIG. 6 shows a design of a process 600 performed by a transmitter totransmit pilot to a receiver. Process 600 may be performed by a terminalto transmit pilot on the reverse link to a base station. Process 600 mayalso be performed by a base station to transmit pilot on the forwardlink to terminals. The transmitter may thus be a terminal or a basestation, and the receiver may be a base station or a terminal. Pilotsymbols for a first cluster in a time frequency block (or tile) may begenerated based on a first sequence (block 612). Pilot symbols for asecond cluster in the time frequency block may be generated based on asecond sequence (block 614). Pilot symbols for a third cluster in thetime frequency block may be generated based on the first sequence or athird sequence (block 616). Pilot symbols for a fourth cluster in thetime frequency block may be generated based on the second sequence or afourth sequence (block 618). The pilot symbols may be transmitted intheir respective clusters (block 620).

The first, second, third and fourth sequences may include commonelements arranged in different orders and may be considered as differentversions of a single sequence. For example, the elements in the secondsequence may be in a reverse order (or flipped) with respect to theelements in the first sequence. The pilot symbols may be generated suchthat they are symmetric about the center of the time frequency block,e.g., as shown in FIGS. 5A through 5D. The pilot symbols in all clustersmay also be arranged in other manners, possibly non-symmetric manners.Each sequence may include M elements used to generate M pilot symbolsfor one cluster, where M may be three, four, etc. Each sequence mayinclude elements in a column of a Fourier matrix or elements defined inother manners.

For the reverse link, the first sequence may be assigned to a terminaland may be orthogonal to at least one other sequence assigned to atleast one other terminal sharing the first cluster. Similarly, thesecond, third, and fourth sequences may be assigned to the terminal.Each sequence assigned to the terminal may be orthogonal to othersequence(s) assigned to other terminal(s) for the cluster in which thatsequence is used. For the forward link, the first sequence may beassigned to a layer and may be orthogonal to at least one other sequenceassigned to at least one other layer for the first cluster.

FIG. 7 shows a design of an apparatus 700 for transmitting pilot.Apparatus 700 includes means for generating pilot symbols for a firstcluster in a time frequency block based on a first sequence (module712), means for generating pilot symbols for a second cluster in thetime frequency block based on a second sequence (module 714), means forgenerating pilot symbols for a third cluster in the time frequency blockbased on the first sequence or a third sequence (module 716), means forgenerating pilot symbols for a fourth cluster in the time frequencyblock based on the second sequence or a fourth sequence (module 718),and means for transmitting the pilot symbols in their respectiveclusters (module 720). The first, second, third and fourth sequences mayinclude common elements arranged in different orders. Modules 712 to 720may comprise processors, electronics devices, hardware devices,electronics components, logical circuits, memories, etc., or anycombination thereof.

FIG. 8 shows a design of a process 800 performed by a receiver toprocess pilot received from one or more transmitters. Process 800 may beperformed by a base station to process pilot received on the reverselink from one or more terminals. Process 800 may also be performed by aterminal to process pilot received on the forward link from a basestation for one or more layers, where each layer may be considered as aseparate transmitter. The receiver may thus be a base station or aterminal, and the transmitter may be a terminal or a base station.Received pilot symbols may be obtained from multiple clusters in a timefrequency block (block 812). Each of multiple basis vectors may beformed with multiple versions of a sequence assigned to a transmitter(block 814). The sequence may include M elements, and the multipleversions of the sequence may correspond to different orderings of the Melements in the sequence. The multiple basis vectors may be formedfurther based on a particular channel model, e.g., a channel model withlinearly varying time component and linearly varying frequencycomponent, as shown in equation (7). The received pilot symbols may beprocessed with the multiple basis vectors to obtain a channel estimatefor the transmitter, e.g., as shown in equations (8) and (11) (block816). The received pilot symbols may also be processed with at least oneother basis vector to obtain a noise and interference estimate, e.g., asshown in equations (8) and (9) (block 818).

For block 814, each basis vector may be formed based on an originalversion and a flipped version of the sequence, e.g., as shown inequation (22). Alternatively, each basis vector may be formed based onfour versions of the sequence, e.g., as shown in equation (23). In anycase, the multiple versions of the sequence may be used to generatepilot symbols for the multiple clusters such that the pilot symbols aresymmetric about the center of the time frequency block.

For block 816, multiple complex values (e.g., w_(i,q)) may be obtainedbased on dot products of the received pilot symbols with the multiplebasis vectors, e.g., as shown in equation (8). The multiple complexvalues may comprise a first complex value indicative of an averagechannel gain for the time frequency block, a second complex valueindicative of channel variation across frequency, and a third complexvalue indicative of channel variation across time. The channel estimatefor the transmitter may be derived based on the multiple complex values,e.g., as shown in equation (11).

FIG. 9 shows a design of an apparatus 900 for processing received pilot.Apparatus 900 includes means for obtaining received pilot symbols frommultiple clusters in a time frequency block (module 912), means forforming each of multiple basis vectors with multiple versions of asequence assigned to a transmitter (module 914), means for processingthe received pilot symbols with the multiple basis vectors to obtain achannel estimate for the transmitter (module 916), and means forprocessing the received pilot symbols with at least one other basisvector to obtain a noise and interference estimate (module 918). Themultiple versions of the sequence may correspond to different orderingsof elements in the sequence. Modules 912 to 918 may comprise processors,electronics devices, hardware devices, electronics components, logicalcircuits, memories, etc., or any combination thereof.

The techniques described herein may be implemented by various means. Forexample, these techniques may be implemented in hardware, firmware,software, or a combination thereof. For a hardware implementation, theprocessing units at an entity (e.g., a terminal or a base station) maybe implemented within one or more application specific integratedcircuits (ASICs), digital signal processors (DSPs), digital signalprocessing devices (DSPDs), programmable logic devices (PLDs), fieldprogrammable gate arrays (FPGAs), processors, controllers,micro-controllers, microprocessors, electronic devices, other electronicunits designed to perform the functions described herein, a computer, ora combination thereof.

For a firmware and/or software implementation, the techniques may beimplemented with modules (e.g., procedures, functions, etc.) thatperform the functions described herein. The firmware and/or softwareinstructions may be stored in a memory (e.g., memory 142 x, 142 y or 182in FIG. 1) and executed by a processor (e.g., processor 140 x, 140 y or180). The memory may be implemented within the processor or external tothe processor. The firmware and/or software instructions may also bestored in other processor-readable medium such as random access memory(RAM), read-only memory (ROM), non-volatile random access memory(NVRAM), programmable read-only memory (PROM), electrically erasablePROM (EEPROM), FLASH memory, compact disc (CD), magnetic or optical datastorage device, etc.

The previous description of the disclosure is provided to enable anyperson skilled in the art to make or use the disclosure. Variousmodifications to the disclosure will be readily apparent to thoseskilled in the art, and the generic principles defined herein may beapplied to other variations without departing from the spirit or scopeof the disclosure. Thus, the disclosure is not intended to be limited tothe examples described herein but is to be accorded the widest scopeconsistent with the principles and novel features disclosed herein.

What is claimed is:
 1. An apparatus comprising: a processor configuredto obtain received pilot symbols from multiple clusters in a timefrequency block, to form each of multiple basis vectors with multipleversions of a sequence assigned to a transmitter, and to process thereceived pilot symbols with the multiple basis vectors, wherein theprocessor is configured to form each basis vector based on four versionsof the sequence used to generate pilot symbols for the multipleclusters, the pilot symbols being symmetric about a location that isclose to a center of the time frequency block; and a memory coupled tothe processor.
 2. The apparatus of claim 1, wherein the multipleversions of the sequence correspond to different orderings of elementsin the sequence.
 3. The apparatus of claim 1, wherein the processor isconfigured to form each basis vector based on an original version and aflipped version of the sequence.
 4. The apparatus of claim 1, whereinthe processor is configured to form the multiple basis vectors furtherbased on a channel model with linearly varying time component andlinearly varying frequency component.
 5. The apparatus of claim 1,wherein the processor is configured to obtain multiple complex valuesbased on dot products of the received pilot symbols with the multiplebasis vectors, and to derive a channel estimate for the transmitterbased on the multiple complex values.
 6. The apparatus of claim 5,wherein the multiple complex values comprise a first complex valueindicative of an average channel gain for the time frequency block. 7.The apparatus of claim 6, wherein the multiple complex values comprise asecond complex value indicative of channel variation across frequencyand a third complex value indicative of channel variation across time.8. The apparatus of claim 1, wherein the processor is configured toobtain at least one complex value based on dot product of the receivedpilot symbols with at least one other basis vector, and to derive anoise and interference estimate based on the at least one complex value.9. A method comprising: obtaining received pilot symbols from multipleclusters in a time frequency block; forming each of multiple basisvectors with multiple versions of a sequence assigned to a transmitter,the pilot symbols being symmetric about a location that is close to acenter of the time frequency block; and processing the received pilotsymbols with the multiple basis vectors transmitter.
 10. The method ofclaim 9, wherein the multiple versions of the sequence correspond todifferent orderings of elements in the sequence.
 11. he method of claim9, wherein the processing the received pilot symbols with the multiplebasis vectors comprises: obtaining multiple complex values based on dotproducts of the received pilot symbols with the multiple basis vectors,and deriving a channel estimate for the transmitter based on themultiple complex values.
 12. The method of claim 11, wherein themultiple complex values comprise a first complex value indicative of anaverage channel gain for the time frequency block, a second complexvalue indicative of channel variation across frequency, and a thirdcomplex value indicative of channel variation across time.
 13. Themethod of claim 9, further comprising: obtaining at least one complexvalue based on dot product of the received pilot symbols with at leastone other basis vector; and deriving a noise and interference estimatebased on the at least one complex value.
 14. An apparatus comprising:means for obtaining received pilot symbols from multiple clusters in atime frequency block; means for forming each of multiple basis vectorswith multiple versions of a sequence assigned to a transmitter, thepilot symbols being symmetric about a location that is close to a centerof the time frequency block; and means for processing the received pilotsymbols with the multiple basis vectors.
 15. The apparatus of claim 14,wherein the means for processing the received pilot symbols with themultiple basis vectors comprises means for obtaining multiple complexvalues based on dot products of the received pilot symbols with themultiple basis vectors, and means for deriving a channel estimate forthe transmitter based on the multiple complex values.
 16. The apparatusof claim 14, further comprising: means for obtaining at least onecomplex value based on dot product of the received pilot symbols with atleast one other basis vector; and means for deriving a noise andinterference estimate based on the at least one complex value.
 17. Aprocessor-readable medium including instructions stored thereon,comprising: a first instruction set for obtaining received pilot symbolsfrom multiple clusters in a time frequency block;